That's exactly the behavior of our TechLite Lumen Master flashlight. Maybe there is a mass-produced flashlight chip that you can buy, or you can harvest the circuit from a flashlight?

Alternatively, why not use an MCU? A simple one like a PICAXE 08M2 is capable of doing what you want, including debouncing the pushbutton. Not that hard to learn, and trivial to program (you just use BASIC). Comes in an 8-pin DIP, that's pretty simple and small. No external oscillators. About all you would need is an external pass transistor to handle the current of your LED.